Dose-escalation Study of Safety of PBCAR20A in Subjects With r/r NHL or r/r CLL/SLL

This is a multicenter, nonrandomized, open-label, parallel assignment, single-dose, dose-escalation, and dose-expansion study to evaluate safety, tolerability, clinical activity, and find an appropriate dose to optimize safety and efficacy of PBCAR20A in subjects with relapsed/refractory (r/r) CD20+ Non-Hodgkin Lymphoma (NHL) or r/r Chronic Lymphocytic Leukemia (CLL) or Small Lymphocytic Lymphoma (SLL). Before initiating PBCAR20A, therapy, subjects will be administered lymphodepletion chemotherapy composed of fludarabine and cyclophosphamide. At Day 0 of the Treatment Period, subjects will receive a single intravenous (IV) infusion of PBCAR20A. All subjects are monitored during the treatment period through Day 28. All subjects who receive a dose of PBCAR20A will be followed in a separate long-term follow-up (LTFU) study for 15 years after exiting this study.